Download They might be giants: luminosity class, planet frequency, and planet

Accepted to ApJ
Preprint typeset using LATEX style emulateapj v. 11/10/09
THEY MIGHT BE GIANTS:
LUMINOSITY CLASS, PLANET OCCURRENCE, AND PLANET-METALLICITY RELATION OF THE
COOLEST KEPLER TARGET STARS
Andrew W. Mann1 , Eric Gaidos2 , Sébastien Lépine3 , Eric J. Hilton2
arXiv:1202.5394v2 [astro-ph.EP] 5 May 2012
Accepted to ApJ
ABSTRACT
We estimate the stellar parameters of late K and early M type Kepler target stars. We obtain
medium resolution visible spectra of 382 stars with KP − J > 2 (≃ K5 and later spectral type).
We determine luminosity class by comparing the strength of gravity-sensitive indices (CaH, K I, Ca
II, and Na I) to their strength in a sample of stars of known luminosity class. We find that giants
constitute 96 ± 1% of the bright (KP < 14) Kepler target stars, and 7 ± 3% of dim (KP > 14) stars,
significantly higher than fractions based on the stellar parameters quoted in the Kepler Input Catalog
(KIC). The KIC effective temperatures are systematically (110+15
−35 K) higher than temperatures we
determine from fitting our spectra to PHOENIX stellar models. Through Monte Carlo simulations of
the Kepler exoplanet candidate population, we find a planet occurrence of 0.36 ± 0.08 when giant stars
are properly removed, somewhat higher than when a KIC log g > 4 criterion is used (0.27 ± 0.05).
Lastly, we show that there is no significant difference in g − r color (a probe of metallicity) between
late-type Kepler stars with transiting Earth-to-Neptune sized exoplanet candidates and dwarf stars
with no detected transits. We show that a previous claimed offset between these two populations is
most likely an artifact of including a large number of misidentified giants.
Subject headings: Planets and satellites: detection, Planetary systems, Stars: fundamental parameters,
Stars: late-type, Stars: abundances, Stars: AGB and post-AGB
1. INTRODUCTION
The NASA Kepler mission (Borucki et al. 2010) has
ushered exoplanet science into a new phase of analysis
based on the statistics of large samples. Among the
more elementary statistics derived from Kepler results
are the planet occurrence around stars (Howard et al.
2011, henceforth H11), the distribution of planet size
(or mass Wolfgang & Laughlin 2011; Gaidos et al. 2012),
correlations between the presence of planets and the
properties of the host stars (e.g. Schlaufman & Laughlin
2011, henceforth SL11), and the characteristics of multiplanet systems (Fabrycky et al. 2012). These findings
yield important constraints on models of planet formation and evolution, and are best established for solar-type
stars (late F through early K spectral types) because they
constitute the vast majority of Kepler targets.
The results of Kepler were first preceded by the findings of radial velocity surveys of solar-type stars. More
than 15% of dwarf stars have close-in (∼0.25 AU) planets with orbital periods less than 50 days (Howard et al.
2010, 2011) and this fraction increases with orbital period
(Mayor et al. 2011). The same authors find that planet
occurrence is inversely related to planet mass or radius,
with “super-Earths” outnumbering Jupiter-size planets
by more than an order of magnitude. Around solar-type
stars, the presence of giant planets is strongly correlated
with super-solar metallicity (Gonzalez 1997; Santos et al.
2004; Fischer & Valenti 2005; Johnson et al. 2010), but
1 Institute for Astronomy, University of Hawai’i, 2680 Woodlawn Dr, Honolulu, HI 96822
2 Department of Geology & Geophysics, University of Hawai’i,
1680 East-West Road, Honolulu, HI 96822
3 Department of Astrophysics, American Museum of Natural
History, New York, NY 10024
this correlation does not appear to hold for smaller planets (Sousa et al. 2008; Bouchy et al. 2009; Mayor et al.
2011). As with results from Kepler, these findings are
primarily for solar-type stars because many nearby representatives are bright enough for ground-based Doppler
radial velocity observations.
Very cool (late K and early M type) dwarf stars
have become popular targets of planet searches (e.g.
Charbonneau et al. 2009; Vogt et al. 2010; Bean et al.
2010; Mann et al. 2011; Apps et al. 2010; Fischer et al.
2012). Planets around cool stars are easier to detect
because of the stars’ smaller masses and radii. Furthermore, because these stars are less luminous, close-in and
thus detectable planets can still orbit within the “habitable zone,” where an Earth-like planet would avoid
the “snowball” or runaway greenhouse climate states
(Gaidos et al. 2007). However, the statistics of planets
around these stars are poorly established. These stars
are underrepresented in magnitude-limited Doppler surveys as well as the Kepler target list. Only 2% of Kepler target stars are classified as possible M types (cooler
than 4000 K), whereas >70% of all stars within 20 pc are
M dwarfs (Henry et al. 1994; Chabrier 2003; Reid et al.
2004).
Nevertheless, Kepler data has been used to draw two
important conclusions about late-type exoplanet hosts.
First, H11 found that the frequency of stars with planets
on close-in (P< 50d) orbits rises with decreasing effective temperature through early K-type and that an even
higher fraction of M dwarf stars may host such planets.
Second, SL11 claimed that late K dwarf stars, but not
solar-type stars, hosting super-Earth to Neptune sized
candidate transiting planets are more metal rich than
stars for which transits have not been detected. These
2
Mann et al.
findings offer potential tests of theories of planet formation (Fischer & Valenti 2005; Kennedy & Kenyon 2008;
Cumming et al. 2008)
Kepler targets are selected from the Kepler input catalog (KIC) based on the ability of the mission to find
transiting planets, especially in the habitable zone; ideally, the target catalog should consist exclusively of dwarf
stars for which the signal of a transiting planet is largest,
and exclude sub-giant and giant stars. Brown et al.
(2011) used D51 (Mg Ib line) photometry and Sloan gD51 color to exclude giants, however this is also sensitive
to temperature and metallicity and is not available for
all targets. The KIC includes Sloan (griz) and 2MASS
(JHK) magnitudes; stellar parameters are estimated by
forward modeling of the photometric data with the synthetic spectra of Castelli & Kurucz (2004), and effective
temperature Tef f , gravity log g, and metallicity [M/H] as
free parameters. Stellar mass and distance are then estimated using luminosity, Tef f , and log g from the stellar
evolutionary models of Girardi et al. (2000). The combination of stellar mass and log g then yields a stellar
radius.
Brown et al. (2011) state that KIC radius estimates
have average errors of 35% and are not reliable for stars
cooler than 4000 K. H11 point out that, because of the
difficulty in constraining log g, the radii of some stars,
particularly sub-giants, may be underestimated by a factor of 2 or more in the KIC. Gaidos et al. (2012) found
that consistency between the Kepler candidate planet
catalog and the M2K Doppler survey could be achieved if
the former was incomplete compared to estimates based
on KIC radii. They further point out that Kepler planet
candidates were conspicuously sparse among late K stars
with colors that are shared by both dwarfs and giant
stars. Finally, Muirhead et al. (2012) (henceforth M11)
showe that KIC estimates for the radii of many Kepler
M dwarfs hosting planets are smaller than KIC values
by as much as a factor of two. This discrepancy is not
to be confused with the 5-10% radius difference between
radii of the most refined models and measurements by interferometry and observations of eclipsing binaries (e.g.
López-Santiago et al. 2010; Kraus et al. 2011).
Reliable stellar parameters are a prerequisite for robust
statistical analysis of planets, especially transiting planets. These are needed not only for stars for which planet
candidates have been detected (referred to as Kepler Objects of Interest or KOIs), but also for the target sample
as a whole. The radius of a planet producing a given
transit depth is proportional to the radius of its host
star. Likewise, the transit signal produced by a planet
of a given radius - and hence its detectability around a
star in the survey - also depends on stellar radius. If
some target stars are actually larger or even giant stars,
then planets are less likely to be detected in that sample, which means that the most likely occurrence rate of
those planets is higher. For M dwarf stars in general, and
particularly for the coolest Kepler target stars, parameters such as radius are uncertain or even very unreliable
(e.g. Johnson et al. 2012, M11).
Brown et al. (2011) metallicities are reliable to 0.4 dex
for solar-type stars, but are essentially useless for stars
with Tef f < 4000. Instead, SL11 use Sloan g − r colors for a given J − H range (a proxy for spectral type)
as an indicator of the amount of Fe line blanketing at
blue wavelengths, and hence metallicity. They construct
mean g − r vs. J − H loci for KOIs and Kepler stars
without identified transits. They find a significant difference between the g − r colors of the two populations
for stars with J − H ≈ 0.62, corresponding to late Ktype stars. Based on stellar models, SL11 argue that
the late-type KOIs are ≃ 0.2 dex more metal rich than
Kepler targets with no detected transit. However, K giants are significantly bluer than dwarfs in g − r, for the
same J − H (Yanny et al. 2009). Thus, contamination of
the Kepler target sample by giants would shift the locus
of target stars to bluer g − r, but would not affect the
KOI locus, as planets are less detectable, or completely
undetectable around giant stars. Realizing this, SL11
constructed and analyzed artificial mixed data sets to
estimate that a 10-30% contamination by giants would
also produce the observed offset.
M11 use the equivalent widths of atomic lines in the
K (2.2 µm) band (Rojas-Ayala et al. 2012) and their
measurements of late-type KOIs’ metallicities are consistent with, or slightly metal-poor (median [M/H] = 0.10) compared to the solar neighborhood (M/H ≃ −0.05
Johnson & Apps 2009). SL11 and M11 are consistent
with each other if the Kepler target list itself is biased
toward metal-poor M dwarfs, or if the offset found by
SL11 is due to high giant contamination in Kepler latetype target stars.
Moderate resolution spectra are nearly always sufficient to distinguish K and M giants from their dwarf
cousins. In addition Ciardi et al. (2011) showed that
some giant stars can be identified based on JHK photometry alone. In this paper, we combine moderate resolution spectra of a sample of Kepler targets with KIC
photometry to refine the planet occurrence rate for latetype stars calculated by H11, and determine if the giant
fraction is high enough to explain the color offset observed by SL11. In Section 2 we present spectroscopy of
a representative sample of late-type Kepler target stars.
In Section 3 we use both spectroscopy and photometry
to derive luminosity classes and calculate the giant fraction for late-type Kepler target stars. In Section 4 we
use this information, plus radii based on stellar evolutionary models, to refine the planet occurrence around
these stars. In Section 5 we calculate and compare the
mean g − r colors (as metallicity proxies) of KOIs and
a bona fide dwarf sample, and show how and why our
results differ from those of SL11.
2. SAMPLE, OBSERVATIONS, AND REDUCTION
Because derived KIC parameters may not always be
reliable, we instead select our sample using photometry.
A sample of stars with V − J > 2.5 will include > 98%
of all M dwarfs, as well as most of the K7 dwarfs in the
sample (Lépine & Gaidos 2011, henceforth LG11). Although 2MASS J magnitudes are available for almost the
entire sample, V magnitudes are not. Kepler magnitudes
(KP ), however, are available for all target stars. For M0
stars, KP − V ≃ −0.434 so we conservatively select stars
with Kp − J > 2 observed in Quarters 0-2 by Kepler
and retrieved from the Multimission Archive (STScI).
We remove stars with a contaminating star within 1 arc
second.
4
keplergo.arc.nasa.gov/CalibrationZeropoint.shtml
Parameters of the Coolest Kepler Targets
3
Fig. 1.— Kepler magnitude vs. J − H color for Quarter 0-2
Kepler target stars with KP − J > 2 (grey circles), KOIs (black
stars), and targets with spectra from this program (red circles).
Our observing bins (see Section 2) are marked by blue lines. There
is a clear difference between the colors of bright (KP < 14) and
dim (KP > 14) Kepler target stars, resulting in a very different
distribution of colors. The great majority of KOIs are faint, and
have bluer J − H colors. For this reason we divide the sample into
J −H bins, and treat bright (KP < 14) and dim (KP > 14) Kepler
target stars as two independent samples.
Fig. 2.— Distribution of KIC effective temperatures and KP − J
colors for target stars (grey circles and grey solid histogram) and
KOIs (black stars and black dashed histogram). The bulk of the
stars in our spectroscopic sample are M dwarfs (Tef f < 4000 K) if
we assume KIC Tef f values are accurate. Histograms for KOIs and
observe targets offset slightly from each other for clarity (although
the bins for each sample are the same). Note that not all stars
have effective temperatures listed in the KIC; points lacking Tef f
values are not shown in the center plot or bottom histogram, but
are included in the KP − J histogram.
Bright Kepler target stars were selected in a fundamentally different way from dim stars (see Figure 1
and Batalha et al. 2010). We separately analyzed dim
(KP > 14) and bright (KP < 14) stars. Bessell & Brett
(1988) showed that giant stars tend to have more extreme
J − H colors than their dwarf counterparts. However,
we wanted to investigate how misidentified giant stars in
the KIC are distributed with J − H color. Thus we further subdivided our sample into four J − H color bins:
J − H ≤ 0.70, 0.70 < J − H ≤ 0.76, 0.76 < J − H ≤ 0.82,
and 0.82 < J − H for the bright stars and J − H ≤ 0.62,
0.62 < J − H ≤ 0.65, 0.65 < J − H ≤ 0.68, and
J − H > 0.68 for the dim stars. Color bins were designed
such that each contains a similar number of stars. We
observed a sample of stars within each bin, selected randomly with respect to J − H. We observed more bright
stars because they are more observationally accessible,
although we observed targets spanning all Kepler magnitudes to detect trends with KP . In total we observed
382 stars covering 6.5 < KP < 16, 0.40 < J − H < 1.00
and KIC effective temperatures 3200 < Tef f < 5050 K.
The distribution of observed targets is shown in J − H
and KIC Tef f space in Figure 2. A list of observed targets is given in Table 1.
Observations were obtained between June 16 and Aug
28 (2011) with the SuperNova Integral Field Spectrograph (SNIFS, Lantz et al. 2004) at the University of
Hawaii 2.2m telescope on Mauna Kea and the Boller
and Chivens CCD Spectrograph (CCDS) or the Mark
III spectrograph (MkIII) at the MDM Observatory 1.3m
McGraw-Hill telescope on Kitt Peak. SNIFS is an optical
integral field spectrograph with R ≃ 1300 that splits the
signal with a dichroic mirror into blue (3000 − 5200 Å)
and red (5000 − 9500 Å) channels. SNIFS images were
resampled with microlens arrays, dispersed with grisms,
and focused onto blue- and red-sensitive CCDs. Processing of SNIFS data was performed with the SNIFS
pipeline, described in detail by Aldering et al. (2006) and
Pereira et al. (2010). SNIFS processing included dark,
bias, and flat-field corrections, assembling the data into
red and blue 3D data cubes, and cleaning them for cosmic
rays and bad pixels. After sky subtraction, the spectra
are extracted with a PSF model, and wavelengths were
calibrated with arc lamp exposures taken at the same
telescope pointing as the science data.
The CCDS and MkIII spectrographs cover 5700 −
9300Å and 4400 − 8300Å with R ≃ 1150 and ≃ 2300,
respectively. Standard reduction of data taken with the
CCDS and MkIII was performed with IRAF, following
the practice of overscan subtraction, division by flat field,
and extraction of the spectra. Spectra were wavelengthcalibrated against NeArXe comparison arcs. All observations (including SNIFS) were flux-calibrated and telluric lines were removed based on observations of the
NOAO primary spectrophotometric standards Feige 66,
Feige 110, and BD+284211. All spectra had a median
S/N of > 30 in the 6000-7000Å range, and the median
S/N of all spectra in this range was 50.
Our spectroscopic set only covers KP − J > 2.0, but
we also consider a separate ‘photometric
S sample’ that includes stars with 0.56 < J−H < 0.66 KP −J > 2. This
is done so we can ensure coverage of the sample of late
K stars used by SL11 (see Section 5). The KIC includes
JHK photometry from 2MASS (Skrutskie et al. 2006)
and visible-wavelength photometry through SDSS griz
and D51 filters. We add photometry from the Wide-field
Infrared Survey Explorer (WISE, Wright et al. 2010),
which includes 3.4µm, 4.6µm, 12µm, and 22µm bands.
3. LUMINOSITY CLASS
We determine luminosity class by comparing the spectral indices or colors of Kepler target stars to those
of stars drawn from ‘training sets’ of known giants or
dwarfs. We first discuss how we construct our training
sets. We then explain our choice of indices and colorcolor relations, based on previous work on giant/dwarf
discrimination and derived empirically from examination
of the differences between the dwarf and giant training
4
Mann et al.
TABLE 1
Parameters of Observed Kepler Targetsa
KIC Parameters
Derived from Spectra
KIC ID
KP
log g Tef f [K] Instrumentb Luminosity Classc Tef f [K] σT [K]
3001835d
13.5 —
—
SNIFS
Giant
3800
60
8881126
15.8 4.6
3890
SNIFS
Dwarf
3720
60
10717091d 10.3 —
—
MkIII
Giant
3790
60
10406398d 15.9 —
—
SNIFS
Giant
3310
100
8426324
10.3 2.2
3526
CCDS
Giant
3480
90
3455941d
10.9 —
—
CCDS
Giant
4260
40
6032907
15.3 4.5
3938
SNIFS
Dwarf
3830
70
10064712d 9.4
—
—
CCDS
Giant
4050
60
5112438d
10.7 —
—
MkIII
Giant
3600
70
5732026d
9.5
—
—
MkIII
Giant
3860
70
10593779d 8.9
—
—
CCDS
Giant
3930
60
4818175d
7.6
—
—
CCDS
Giant
3930
50
9175009
14.2 4.6
3836
SNIFS
Dwarf
3870
70
12417370
9.0
2.5
4098
CCDS
Giant
3900
60
10843322
15.0 4.4
3650
SNIFS
Dwarf
3580
80
6695442d
13.4 —
—
SNIFS
Giant
3630
70
...
Note.
— a The complete table is available in the electronic version of Astrophysical Journal and at
http://ifa.hawaii.edu/~ amann/Table1_full.txt.This table is provided for guidance on the fields and format.
b SNIFS = SuperNova Integral Field Spectrograph, CCDS = Boller & Chivens CCD Spectrograph, MkIII = Mark III spectrograph. SNIFS
is attached to the University of Hawaii 2.2-meter telescope, and both CCDS and MkIII at the MDM Observatory 1.3m McGraw-Hill
Telescope.
c Luminosity classes derived based on our spectra.
d No temperatures or log g values present in the KIC
set. We use the colors and spectroscopic indices of stars
in the training sets to construct a likelihood estimator,
such that we can calculate the likelihood that a given
star is a giant (or dwarf). That calculation is explained
in Section 3.4.
3.1. Training Sets
We construct an uncontaminated set of dwarf stars
from a sample of high proper motion-selected late dK
and dM stars (LG11). The brightest (J < 9) northern stars in the LG11 catalog have visible-wavelength
spectra (Lépine et al. in prep), obtained with the same
instruments and reduced in the same way as was done
for Kepler targets observed for this paper. Although the
sample from Lépine et al. (in prep) includes more than
1500 spectra, we construct our dwarf sample only from
the 620 targets with spectra from SNIFS/UH2.2m, which
includes the Ca II triplet feature at 8484 − 8662Å.
LG11 use J − H, and H − K colors, combined with
proper motion from SUPERBLINK (Lépine & Shara
2005) and (for some targets) parallax information from
Hipparcos (van Leeuwen & Fantino 2005; van Leeuwen
2007) to remove giant stars. Based on those stars in
LG11 with parallaxes, we estimate that fewer than 0.5%
of the resulting sample will be giants. However, because
of strict cuts in J − H and H − K, the LG11 sample is incomplete and biased against dwarfs with much
redder or bluer colors. LG11 also use a color cut of
V − J > 2.7 to select mostly M dwarfs. This excludes
some mid- to S
late-K stars which will be included in our
(KP − J > 2 0.58 < J − H < 0.66) color cut for the
photometric sample (see Section 2). We therefore add
60 late K and early M dwarfs included in the Hipparcos catalog that have UH2.2m spectra but lie outside the
cuts imposed by LG11. These stars are confirmed to be
dwarfs by their Hipparcos parallaxes. We also add 150
M dwarfs with spectra from SDSS, including 50 dwarf
from West et al. (2011), with r − J and J − H colors
consistent with our targets of interest. We verify that
these targets are dwarfs using a cut with reduced proper
motion, where the reduced proper motion in the SDSS g
band is:
Hg = g + 5 log µ + 5,
(1)
and µ is the proper motion in arcsec yr−1 . This quantity is similar to the absolute magnitude, such that giant
stars will have much lower reduced proper motions than
dwarfs of the same color. We only select SDSS stars with
Hg > 2.2(g − r) + 7.0, and µ > 15 arcsec yr−1 , which
we determine empirically from our UH2.2m targets with
SDSS photometry.
Our sample of >300 giant spectra is constructed
from multiple catalogs, specifically Fluks et al. (1994),
Danks & Dennefeld (1994), Allen & Strom (1995),
Serote Roos et al. (1996), Montes et al. (1999), and
Lançon & Wood (2000), as well as 80 bright stars we
observed with UH2.2/SNIFS that are confirmed to be
giants by Hipparcos. Many spectra have significantly
higher resolution than our own observations. We convolve these data with a gaussian to match the resolution
of our own sample to remove any resolution-dependency
in our results. To include sufficient SDSS photometry,
we supplement our giant training set by including 200
giant stars with spectra from SDSS all with r < 16 and
proper motions consistent with zero. We require these
SDSS spectra to have spectroscopic indices consistent
with the rest of the giant training set. Because we
select only SDSS stars with indices consistent with
indices from spectra from the rest of the training stars,
SDSS giant stars have no effect on our spectroscopic
determination of luminosity class. Rather, these SDSS
stars are added only for their photometry.
SDSS, 2MASS and WISE colors are available for much
Parameters of the Coolest Kepler Targets
5
cially for M stars which emit comparatively more at red
wavelengths. Giant and dwarf training sets overlaid on
Kepler target star indices are shown in Figure 4.
3.3. Photometric Determination of Luminosity Class
Fig. 3.— SNIFS spectra of an M dwarf (top) and M giant (bottom) of similar Tef f (≃ 3600 K) and magnitude (KP ≃ 14). Approximate regions for each of the six indices we use for giant/dwarf
discrimination, as well as the TiO5 band, are marked in grey. B
1 refers to a mix of atomic lines (Ba II, Fe I, Mn I, and Ti I)
which overlap at the resolution of SNIFS (≃ 1300). The TiO5
molecular band is used as a probe of spectral type, although it
is also sensitive to metallicity (Lépine et al. 2007). Other atomic
and molecular lines are generally much weaker in late type giant
stars (Reid & Hawley 2005). Indeed, the Na I (8172-8197Å) and
K I (7669-7705Å) doublets are significantly weaker in the giant
spectrum while they are both quite strong in the dwarf.
of our giant and dwarf training set; however, most
lack D51 photometry, which covers the gravity-sensitive
Mg Ib line at 5200Å. Instead, we synthesize equivalent
g − D51 colors from the spectra of our training set. We
obtain the zero point for the synthesized colors of those
stars in our sample which have both spectra and g and
D51 magnitudes.
3.2. Spectroscopic Determination of Luminosity Class
Our determination of luminosity class uses six different gravity-sensitive molecular or atomic indices (Table
2 and Figure 3). Molecular and atomic indices are ratios
of the average flux levels in a specified wavelength region
to that of a pseudo-continuum region. Indices are useful
for M dwarfs where the continuum is poorly defined. The
values of most indices are a function of both gravity and
temperature of the star. To remove this degeneracy we
compare measured indices to the TiO5 spectral index.
TiO5, as defined by Reid et al. (1995), is sensitive to
spectral type and metallicity (Woolf & Wallerstein 2006;
Lépine et al. 2007) but it has minimal gravity dependance (Jao et al. 2008) (see Figure 3).
We show spectra of giant and dwarf stars with similar effective temperatures in Figure 3, with the location of each feature labeled. As can be seen, most
atomic lines are weaker in giants than in dwarfs. Indeed the Na I doublet (8172-8197Å) and K I (76697705Å) lines are quite shallow in giants while relatively deep in dwarfs (Torres-Dodgen & Weaver 1993;
Schiavon et al. 1997; Reid & Hawley 2005). Molecular
lines provide additional luminosity-dependent spectral
signatures. Metal hydride bands, such as the CaH bands
defined by Reid et al. (1995) and Lépine et al. (2007)
have been used for luminosity classification, although
they are less useful for stars earlier than K7. The calcium
triplet (8484−8662Å) is a useful indicator of gravity (e.g.
Cenarro et al. 2001b; Kraus & Hillenbrand 2009), espe-
We can use the available photometry to determine
the luminosity class of a much larger sample of Kepler
stars lacking spectra. Brown et al. (2011) primarily use
g − D51 vs. g − r and J − K vs. g − i colors to separate Kepler late-type giants from dwarfs. Both giants
and the coolest dwarfs in the sample have relatively weak
Mg Ib lines, creating overlap between the dwarf and giant training sets at red g − r. A similar effect happens
with J − K. Near-infrared photometry (JHK) has long
been used to separate giants and dwarfs at redder colors (Bessell & Brett 1988), in part due to strong CO and
weak Na I and Ca I absorption in giant stars. But for K
and early M stars with J − H < 0.7 and H − K < 0.2,
the giant and dwarf sequences overlap, creating a sizable
region of ambiguity. At mid-infrared wavelengths, most
giant stars have warm dust emission, leading to significantly redder colors in the WISE bandpasses. Other
relations can be derived from an examination of our giant and dwarf training sets. z − K vs. g − J follows a
similar distribution to that of J − K vs. g − i, but the
giant and dwarf samples bifurcate at g − J ≃ 3.0, which
makes this color useful for isolating the reddest giants.
Giant and dwarf training sets overlaid on Kepler target
star colors are shown in Figure 5.
3.4. Application of training sets to the Kepler sample
After each spectral index or color is measured or calculated for Kepler targets and both training sets, we identify stars as giants or dwarfs following the same technique
as Gilbert et al. (2006). We begin by using the spectral
index or color measurements of the training stars to produce a two-dimensional probability distribution function
(PDF) for each index (or color). The PDFs are constructed by treating the strength of each index or color
(henceforth S) as a Gaussian distributed variable with
respect to X. For spectroscopic determination of luminosity class, X is a parameter that primarily relates to
the spectral type (although it may have some gravity dependence), while S is a parameter that primarily relates
to log g. For the spectroscopic determination of luminosity class, X is the TiO5 band and S is one of our
six gravity-sensitive indices (Na I, Ca II, Ba II/Fe I/Mn
I/Ti I, K I, or CaH). For photometric determination of
luminosity class, X is defined as g − J, g − i, J − H,
g − r, 3.4µm - 22µm, or J − 3.4µm and S is z − K,
J − K, H − K, g − D51, 4.6µm - 12µm, or K − 4.6µm,
respectively. Values of S are binned according to their
corresponding X value. Bins in X are designed to contain an equal number of stars (20-25) in each bin, and
because of this are not equally spaced in X. The mean
(S) and standard deviation (σS ) of the distribution is
computed in each bin. The two-dimensional PDF takes
the form:
−(S − S(X))2
,
(2)
P DF (X, S) = Cexp
2(σS (X))2
where C is a normalization such that the entire PDF
integrates to 1. PDFs for both giant and dwarf train-
6
Mann et al.
TABLE 2
Definitions of Spectroscopic Indices
Index Name
Na I (a)
Ba II/Fe I/Mn I/Ti I
CaH2
CaH3
TiO5c
KI
Na I (b)
Ca II
Band [Å]
5868-5918
6470-6530
6814-6846
6960-6990
7126-7135
7669-7705
8172-8197
8484-8662
Continuum [Å]
6345-6355
6410-6420
7042-7046
7042-7046
7042-7046
7677-7691, 7802-7825
8170-8173, 8232-8235
8250-8300, 8570-8600
Sourcea
this workb
Torres-Dodgen & Weaver (1993)
Reid et al. (1995)
Reid et al. (1995)
Reid et al. (1995)
this workb
Schiavon et al. (1997)
Cenarro et al. (2001a)
Note. — Na I, Ba II/Fe I/Mn I/Ti I, K I , and Ca II are measured as equivalent widths, whereas CaH and TiO features are measured
as band indices (Reid et al. 1995).
a Papers where the wavelength definition we use is given.
b Wavelength ranges for Na I (b) and K I were determined from empirical analysis of the giant and dwarf training sets.
c Because TiO5 has minimal gravity dependence, we measure other spectroscopic indices with respect to the TiO5 band strength.
ing sets overlaid on Kepler target star indices or colors
are shown in Figures 4 and 5 for the spectroscopic and
photometric sets, respectively.
The likelihood that star i is a dwarf for a given index
j is:
Pdwarf
Li,j = log10
,
(3)
Pgiant
and the likelihood given all indices is:
P
j wj (X)Li,j
,
hLi i = P
j wj (X)
(4)
where wj is a weighting factor. Weights are calculated
by determining the efficiency of a given feature at separating giants from dwarfs as a function of X. We take
a random subsample (half the total sample) from each
training set, and add Poisson noise to the spectra/colors
consistent with our observations or given photometric errors. We then apply Equations 2 - 4 to the subsamples
using wj (X) = 1 for all X, j. Values of wj are then set
based on the fraction of dwarfs/giants correctly identified within a training set. wj (X) = 1 if the feature/color
identifies 100% of the targets within a given X bin correctly and wj (x) = 0 if the feature/color identifies 50%
or less (i.e. no better than guessing) of the targets correctly. Weights are linearly interpolated (based on the
fraction of stars correctly identified) between these two
values.
Repeating the calculation of Li using wj = 1 for all j
does not change the classification of any stars with spectra (i.e. our results from spectra are essentially independent of our choice of weighting scheme). However, this
is not the case for luminosity classes determined from
color-color relations. The reason for this is the significant overlap between the PDFs of the color metrics for
giant and dwarf training sets (e.g. 2.3 < g − J < 2.8 and
1.6 < z − K < 1.9, see Figure 5). In overlapping regions,
indices or colors will give similar probabilities for a star
being a giant or a dwarf, making the metric less useful
in giant/dwarf discrimination. This problem is solved by
our weighting scheme, as regions where giant and dwarf
training sets overlap tend to have lower weights. We
show a plot of the weights for the color-color relations
in Figure 6. Weighting factors are set to 0 if any of the
relevant indices/colors for a given star are missing or lie
outside the range of our training sets.
We identify all Kepler target stars with spectra as a
giant or a dwarf with better than 99% (Li > 2.0 or
Li < −2.0) confidence. The full list of determined luminosity classes for stars with spectra is given in Table
1. For the photometric sample, ≃ 97% stars are placed
into unambiguous giant or dwarf categories (hLi i > 1.5
for dwarfs or hLi i < −1.5 for giants). However, ≃ 3%
of the sample are more ambiguous, most of which lack
photometry in several bands.
Since giant/dwarf assignments based on spectroscopy
are very accurate, only binomial errors are considered
for the spectroscopic sample. For uncertainty estimates
from the photometric sample, we re-apply our likelihood
calculations using 1000 different subsets of our training
sets, adding random (Poisson) noise to the photometry,
and then recalculating the giant fraction in each case.
The variation in giant fraction is added in quadrature
with binomial errors. This does not consider systematic
errors (e.g. systematic photometric errors, discrepancies
between training sets and Kepler target stars, etc).
3.5. Giant Star Fraction
We find that, for the coolest Kepler stars (KP − J >
2), giant stars dominate the bright (KP < 14) Kepler
target stars but are relatively rare among dim (KP > 14)
targets. The fraction of giants is 96 ± 1% for bright stars,
7 ± 3% for dim stars, and 52 ± 3% for the combined set
(based on our spectroscopy). Photometric assignments
(considering KP − J > 2) give consistent giant fractions:
97 ± 2% for bright stars, 11 ± 3% for dim stars, and
55 ± 3% for all stars with KP − J > 2. The fractions in
each brightness bin decrease somewhat when we apply a
KIC log g > 4.0 cut. The giant fraction becomes 74 ± 8%
for bright stars and 3 ± 2% for dim stars. The fraction
of giants for all stars significantly decreases to 10 ± 2%,
due mainly to the large number of stars lacking any log g
classification, most of which are giants and all of which
are removed by this cut.
4. PLANET OCCURRENCE
Following the work of H11, we calculate the planet occurrence, f , which is defined as the total number of planets, within a given range (in orbital period and radius)
and considering all orbital inclinations, per star within a
given range (in Tef f , log g, and KP ). Planet occurrence
will be somewhat higher than the fraction of stars with
planets due to the presence of multi-planet systems, but
if the rate of planet multiplicity is low, then these two
quantities will be nearly identical.
Parameters of the Coolest Kepler Targets
7
Fig. 4.— Measured strengths of each gravity-sensitive spectral feature vs. the strength of the TiO5 band for Kepler late-type target
stars with spectra from this program. Bright (KP < 14) targets are shown as red colored circles while faint (KP > 14) observed targets
are shown as blue colored circles. The two-dimensional PDFs defined by our training set of giants (dashed line) and dwarfs (solid line)
are overlaid. Contours of the PDF correspond to 68%, and 90%, intervals for the given training set. By using all spectral features, we
positively identify each star with spectra as a giant or a dwarf with > 99% certainty.
4.1. Nonparametric Estimation
We first calculate the planet occurrence following the
nonparametric method of Gaidos et al. (2012). The total planet occurrence, f , is the sum of individual planet
occurrences (fi ) over all i planets that fall within a given
range in orbital period and radius. The most probable
occurrence of the ith Kepler detected planet in the pop-
ulation of j Kepler target stars is:
fi =
1
N
X
,
(5)
pi,j di,j
j=1
where di,j = 1 if the S/N of a planet transit around the
jth star is sufficient to detect the transit, and 0 otherwise, pi,j is the geometric probability of a transit, and j
is summed over all target stars that fall within a given
8
Mann et al.
Fig. 5.— Similar to Figure 4 except using gravity-sensitive color-color relations. Each dot corresponds to a bright (red) or faint (blue)
late-type Kepler target star. Contours are shown for the two training sets, corresponding to 68 and 90% PDF intervals. We apply this
cut to Kepler target stars with J − H > 0.52 or KP − J > 2.0, although only a subsample of this set is shown for clarity. Most stars fall
well inside either the dwarf or giant sequence, however, even when all color relations are used, ≃ 3% of the sample still have an ambiguous
luminosity class assignments. Most of these stars lack photometry in one or more band.
range in Tef f , log g, and KP . We consider a planet detected (di,j = 1) if:
r
Nτ
δ
≥ 7,
(6)
S/N =
σCDP P
30
where δ is the transit depth, N is the number of transits
that occur over the observation interval, τ is the transit duration in minutes, and σCDP P is the 30 minute
combined differential photometric precision (CDPP) of
Kepler. We use Quarter 1-2 30 minute CDPP values
from Kepler. Our detection threshold S/N = 7 matches
what is used by Borucki et al. (2011) and Batalha et al.
(2012).
For small planets on nearly circular orbits,
−1/3
p = 0.238P −2/3M∗
R∗ ,
(7)
where P is the orbital period in days and M∗ and R∗
are the star’s mass and radii in solar units. Values for
M∗ and R∗ are computed by interpolating a grid of stellar radii/masses from the Dartmouth Stellar Evolution
Parameters of the Coolest Kepler Targets
Fig. 6.— Weights for each of the color relations used for our
photometric determination of luminosity class. Weights are determined by applying the giant and dwarf PDFs derived from half
of the training set to the other half (after adding Poisson noise to
the data). Weights are set to 0 for all X outside of our training
sets. Weights tend to be low in regions where the giant and dwarf
training set PDFs overlap, or in regions where data is sparse.
Database (DSEP Dotter et al. 2008) at estimated values of Tef f , [Fe/H], and age. We use DSEP because
radii and masses derived from their isochrones are in
good agreement (< 0.03 RMS deviation in radius) with
current observations from interferometry (Dotter et al.
2008; Feiden et al. 2011).
For exoplanet hosts we use the metallicities given in
M11, but for field stars metallicities are drawn from
a random gaussian distribution of metallicities with
[F e/H] = −0.07 and σ[F e/H] = 0.20. This distribution
is designed to be consistent with the distribution of M
dwarfs in the solar neighborhood (Johnson & Apps 2009;
Casagrande et al. 2011). Ages are assigned randomly assuming a constant star formation rate (excluding ages
< 100 Myr). However, since M dwarfs do not change
significantly while on the main sequence, our results are
not changed when we fix all ages to 5 Gyr. The resulting
stellar radii from the DSEP grid are used in conjunction with values of Rp /R∗ from Borucki et al. (2011) to
compute planetary radii.
Estimates of Tef f are inferred from our optical spectra.
We compare our visible spectra to a grid of models of Kand M-dwarf spectra generated by the BT-SETTL version of PHOENIX (Allard et al. 2010). Details of the
comparison, sub-grid interpolation, and error calculations are described in Lépine et al. (in prep). The grid
of models spans Tef f of 3000-5000 K in steps of 100 K,
log g values of 0.0-5.0 in steps of 0.5 dex, and metallicities of [M/H] = -1.5, -1, -0.5, 0, +0.3, and +0.5. α/Fe
is taken to be solar. We report the Tef f of the best-fit
interpolated model, and the standard deviation of Tef f
among the set of interpolated models that are nearby in
parameter space in Table 1.
Our calculated values of Tef f are shown in Figure 7 vs.
the temperature given in the KIC (Brown et al. 2011).
9
BT-SETTL temperatures are systematically lower than
KIC temperatures by 110+15
−35 K for the dwarf stars,
and 150+10
K
for
the
giant
stars. Errors are calcu−35
lated by bootstrap resampling. This is consistent with
other determinations using the atmospheric models of
Allard et al. (2010), including other determinations on
Kepler KOI stars (M11). Our calculated temperatures
are tightly correlated with KIC temperatures. When
KIC temperatures are corrected for our observed offset,
the standard deviation of the difference in calculated
temperatures (σKIC−P hoenix ) is 90 K, suggesting that
the KIC temperatures for low-mass stars are more precise but are less accurate than suggested by Brown et al.
(2011). For field stars with visible-wavelength spectra,
we adopt our calculated Tef f values, and for stars with
exoplanet candidates we use the Tef f from M11. For
the remaining stars we adjust the KIC effective temperatures of Kepler stars downward randomly by 110+15
−35 K
to keep the temperatures consistent with those of the
KOI stars and those with spectra in our sample. This
offset is randomized to account for errors in the systematic difference between temperatures calculated from our
spectra and those listed in the KIC.
Following H11, we compute the planet occurrence with
2R⊕ < RP < 32⊕ and P < 50 days around stars with
3400 < Tef f < 4100 using Equations 5 - 6. Again
following H11, we exclude stars with KP > 15 where
the accuracy of the planet candidate parameters are
more questionable and the false positive rate is higher
(Morton & Johnson 2011; Borucki et al. 2011). We calculate the standard deviation of the frequency using a
Monte Carlo analysis. Stellar parameters are perturbed
randomly (see above) accounting for errors from M11 on
KOI metallicity and Tef f , and random errors from derived from Tef f fits (see Figure 7) to our spectra. Other
stars are given a random error of 90 K. We perturb transit parameters RP /R∗ and period according to errors
given by Borucki et al. (2011). Planetary radii are recalculated from perturbed values of RP /R∗ and R∗ .
We remove planets from the KOI sample using the false
positive probabilities from Morton & Johnson (2011)
(e.g., a planet candidate with a 5% false positive probability is removed in 5% of the simulations). We remove
giant stars from the sample using the calculated photometric likelihoods (Section 3.3) for each star, such that
a star with a 10% likelihood of being a giant star will
be removed from the sample in 10% of the Monte Carlo
(MC) simulations. This also applies to stars with detected planet candidates, causing the planet to be removed, i.e. we consider the planet detection to be a false
positive if the star is a giant. The number of KOIs and
target stars simulated varies somewhat for each Monte
Carlo run, but there are typically ≃ 14 KOIs around
≃ 1300 stars in a given simulation.
We find that there are 0.37 ± 0.08 planets (with 2R⊕ <
RP < 32R⊕ and P < 50 days) per star in the temperature range 3400 < Tef f < 4100. For comparison we run
an additional Monte Carlo simulation but only remove
giant stars with KIC log g > 4.0 as in H11. This test
yields a planet occurrence of 0.26 ± 0.05, slightly lower
than when giant stars are properly removed. To test how
our results depend on our choice of stellar radii model
(DSEP) we also run two simulations using the Yonsei-
10
Mann et al.
where the first product is of detections, the second is of
non-detections, and ρi is the probability that a planet
with properties in the appropriate ranges orbits the ith
star and is detected by Kepler to transit. For this formulation, we have assumed that ρ ≪ 1. We adopt the
specific power-law form dN = CRi−α P −β d ln R · d ln P
for the intrinsic distribution of planets. If both α and β
are > 0 then the normalization factor C is given by:
C=
R1−α
−
f αβ
,
−β
P1 − P2−β
(9)
R2−α
where f is the total planet occurrence. We do not model
multi-planet systems; that level of analysis is not justified
given the large uncertainties in our parameters.
Following the usual procedure, we maximize the logarithm of L:
D
X
ln L =
[ln C − α ln Rj − β ln Pj + ln Dj (Rj , Pj )]
j
+
ND
X
ln [1 − CFk (α, β)]
(10)
k
where Dj (Rj , Pj ) is the probability of detecting the jth
planet around its host star, including the geometric factor (note Dj (Rj , Pj ) = dj pj , see Equation 5 and 7), and
Z R2 Z P2
R−α P −β Dk (R, P )d ln R · d ln P
Fk (α, β) =
R1
Fig. 7.— Effective temperatures computed by fitting our spectra
to models from the BT-SETTL version of PHOENIX (Allard et al.
2010) as a function of the KIC assigned effective temperature for giants (top) and dwarfs (bottom). The dotted line indicates equality.
Errors are estimated as part of our model fitting procedure (errors
on KIC temperatures are taken to be 135 K (Brown et al. 2011).
For both giants and dwarfs there is a clear 100-200 K offset between
our spectroscopically determined temperatures and the KIC temperatures. This is most likely a consequence of the models used,
as Castelli & Kurucz (2004) models used to fit KIC photometry to
effective temperatures are unreliable below 4000 K.
Yale (Demarque et al. 2004) isochrones: one with giant
stars removed as explained above and another removing
just giants with KIC log g > 4.0. The runs using YonseiYale are included because their models are commonly
used to derive radii for Kepler targets (e.g. Batalha et al.
2012). However, radii and masses derived from DSEP
are a far better match to observations of late-type stars
(Dotter et al. 2008; Feiden et al. 2011), and planet occurrence calculated using the DSEP models should be
considered more reliable. The resulting Monte Carlo distributions are shown in Figure 8.
We also perform a parametric maximum likelihood estimation of the fraction of stars with planets with radii
2R⊕ < R < 32R⊕ and orbital period P < 50 d (see H11
for a similar analysis). For discrete, binomial (detection
or non-detection) events, the likelihood is expressed as:
D
Y
j
ρj ×
N
D
Y
k
(1 − ρk ),
(11)
If the detection rate is low, then:
X
[ln C − α ln Rj − β ln Rj + ln Dj (Rj , PJ )]
ln L ≈
j
−C
ND
X
Fk (α, β).
(8)
(12)
k
We then substitute Equation 9 for C. Ignoring terms
that do not depend on α, and thus do not affect its
maximum likelihood value, we find the following quantity
must be maximized:
X
ln α − ln R1−α − R2−α − α ln Rj −
ln Lα =
j
PN D
k Fk (α, β)
.
−α
−α
R1 − R2
P1−β − P2−β
f αβ
Likewise,
ln Lβ =
(13)
i
Xh
ln β − ln P1−β − P2−β − β ln Pj −
j
PN D
k Fk (α, β)
.
−α
−α
P1−β − P2−β
R1 − R2
f αβ
4.2. Parametric Likelihood estimation
L=
P1
(14)
The simultaneous solution for the planet occurrence is
found by maximizing the terms that depend on f and is
simply
Np R1−α − R2−α P1−β − P2−β
f=
,
(15)
P D
αβ N
Fk (α, β)
k
Parameters of the Coolest Kepler Targets
11
where Np is the number of detected planets. Equation
15 immediately suggests a reduction in the last terms of
Equations 13 and 14 to Np , which is independent of α
and β and can be ignored.
Because there are too few systems in our sample to get
a robust estimate of β, we fix β = 0 with a cut-off at
P1 = 1 d, consistent with the findings of previous analyses (Cumming et al. 2008; Wolfgang & Laughlin 2011,
H11). Equation 15 becomes:
Np R1−α − R2−α ln(P2 /P1 )
.
(16)
f=
PN D
α k Fk (α, β = 0)
Artificial Monte Carlo data sets suggest that f is
robustly recovered, but that recovered values of α are
biased downwards. Using the cool KOIs defined here,
stellar parameters derived as explained above, and
Monte Carlo data sets generated by sampling with
replacement, we find that f = 0.34 ± 0.08, consistent
with our nonparametric calculation. As before, we
repeat our Monte Carlo simulation but only removing
giant stars with KIC log g > 4, and another run using
the Yonsei-Yale evolutionary tracks (Demarque et al.
2004) instead of those of DSEP. The resulting Monte
Carlo distributions are shown in Figure 8.
5. PLANET-HOST METALLICITIES
SL11 use g − r vs. J − H colors to conclude that latetype (J −H ≃ 0.62) exoplanet hosts are redder and more
metal-rich than stars without transiting planets. Because
giant stars have bluer g − r colors at a given J − H color
(Bessell & Brett 1988; Gilbert et al. 2006), a significant
number of giant star interlopers in their sample will cause
field stars to appear metal poor. Giant stars have stellar radii 10-100 times larger than dwarfs, significantly
reducing the depth in a light curve for a given transiting
planet, making it much less likely that they will appear
as KOIs (with the exception of false positives).
We can test their findings by creating a “pure” dwarf
sample, and comparing its color distribution to that of
the KOI sample. Our KP −J > 2 spectroscopic sample is
systematically redder in J − H than the 0.56 < J − H <
0.66 bin used in SL11, preventing us from making a direct comparison. Instead, we construct samples of giants
and dwarfs in the J − H ≃ 0.62 bin based on our photometric determination of luminosity class. For both the
dwarf and giant samples, we select Kepler target stars
with photometry in all bands used in our photometric
assignment of luminosity class (J, H, K, D51, g, r, and all
four WISE bands). We then select stars with a > 90%
likelihood of being dwarfs based on our analysis in Section 3.3. The resulting dwarf sample is ≃ 2500 stars.
This sample may still contain giants. We add Poisson
noise to the photometry of both the training sets and
the Kepler 0.56 < J − H < 0.66 target star sample, and
take random subsamples of both training sets. We then
reapply these subsamples to the modified photometry of
the Kepler sample. We repeat this process 1000 times.
By analyzing the number of giant stars in each of these
new samples we find that our dwarf sample is < 1% giant stars at 95% confidence, ignoring possible systematic
errors.
We use this dwarf sample, following the method of
Fig. 8.— Planet occurrence with giant stars removed (solid line)
or using KIC log g > 4.0, using isochrones from DSEP (black) or
from Yonsei-Yale (red) calculated by Monte Carlo analysis. The
top plot is calculated using nonparametric MC estimate, and the
bottom uses a parametric MC estimate. For both plots, we consider
planets with radii 2R⊕ < RP < 32⊕ and periods P < 50 days,
and stars with effective temperatures 3400 < Tef f < 4100. A full
description of our analysis is given in Section 4.
SL11, to compare the g − r colors at a given J − H
(a proxy of effective temperature) of the exoplanet host
stars with our dwarf sample. Figure 9 shows g − r colors
as a function of J − H colors for the dwarf, giant, planethost, and KIC log g > 4.0 sample. We find no significant
difference in color between the KOI stars and our dwarf
sample. Unlike the KIC log g > 4.0 sample, the locus
of our photometrically selected dwarf sample is consistent with the locus of the KOI sample at J − H ≃ 0.62.
For stars with KP − J > 2.0 we find an offset in g − r
color of only −0.05 ± 0.03 between the spectroscopically
confirmed dwarfs and late-type KOI stars hosting Earthto-Neptune sized planets. When we use our photometric
sample of dwarfs in the J −H ≃ 0.62 bin we find an offset
of 0.01 ± 0.02 and we can rule out the offset of 0.08 seen
by SL11 with > 99.7% certainty. Our photometric selection may remove some metal-poor dwarfs. However, even
when we include stars ≥ 60% likelihood of being dwarfs,
which will necessarily increase the number of interloping
giants, the offset is still only 0.03 ± 0.02 (consistent with
zero offset).
In spite of the low giant fraction for dim Kepler target
stars, it is not sufficient to simply repeat the SL11 analysis exclusively for stars with KP > 14. Since SL11 only
12
Mann et al.
Fig. 9.— Median g − r colors as a function of J − H colors
for Kepler target stars with: Earth to Neptune sized planet candidates (dotted/dashed line, diamonds), KIC log g > 4.0 (solid
line, asterisks), > 90% likelihood of being dwarfs based on their
colors (dotted line, triangles), > 90% likelihood of being giants
(dashed line, circles). The 1σ errors are calculated for the median in each bin by bootstrap resampling. Bins for all data sets
are the same, but each point is offset slightly from the bin center
for clarity. There is a statistically significant offset between the
KIC log g > 4.0 sample and the planet hosts when we consider
stars with 0.58 < J − H < 0.66, however, this offset is no longer
present when misidentified giant stars are removed from the sample. Indeed, our dwarf control sample closely tracks the colors of
the planet-hosting stellar population.
examine stars with KIC log g > 4.0, it is far more important to investigate the g − r distribution of misidentified giants in the 0.56 < J − H < 0.66 color range
(i.e. giant stars that were assigned log g > 4 in the
KIC). In fact the fraction of misidentified dim giant stars
in their J − H ≃ 0.62 bin is higher (12%), than it is
for the KP − J > 2 star sample. We show why this
is the case in Figure 10, which shows the distribution
of giants, dwarfs, and misidentified giants in J − H vs.
g − r space. Misidentified giants are more concentrated
at 0.58 < J − H < 0.63. Further, the misidentified giants
in this J − H range are much more blue than the dwarfs
in the same range. Thus by selecting a color bin centered
on J −H = 0.62, SL11 are over-selecting giant stars, even
after applying a KIC log g > 4 cut (≃ 15% of this sample are giant stars). This concentration of misidentified
giants is the most likely explanation for the color offset
seen by SL11, and also explains why the same g − r offset
is not seen at redder J − H colors (see Figure 9).
6. DISCUSSION
We use visible-wavelength spectra to determine the
properties of a subset of late-type Kepler target stars.
We separate giants from dwarfs by comparing our spectra to those of stars with known luminosity class, and
determine effective temperatures by comparing with
PHOENIX model spectra. We extend our results to a
larger collection of Kepler stars using photometry from
the KIC, 2MASS, and WISE catalogs. We apply our luminosity class determinations to refine estimates of the
planet occurrence around stars with 3400 < Tef f < 4100,
and compare the colors – and hence metallicities of stars
with and without detected Earth and Neptune sized
planets. We draw four major conclusions:
1. Among stars redder than KP − J = 2 (≃ K5 and
later), bright (KP < 14) stars are predominantly (96 ±
1%) giants, while dim stars (KP > 14) are predominantly
(93 ± 3%) dwarfs. These fractions improve somewhat
when we consider stars with KIC determined log g > 4.0
(74 ± 8% and 97 ± 2% respectively). Overall, 52 ± 3%
of Kepler stars with KP − J > 2 are giants. However,
only 10 ± 2% of said stars with KIC log g > 4.0 are
giants, a consequence of the large number of late-type
stars lacking any temperature or log g values in the KIC.
2. KIC effective temperatures, based on the models of
Castelli & Kurucz (2004) and griz and JHK photometry, are systematically higher by 110+15
−35 K compared
to those derived from our own spectra and PHOENIX
BT-SETTL atmosphere models (Allard et al. 2010).
3. Adopting the temperature scale from BT-SETTL
and radii/masses from the Dartmouth Stellar Evolution Database (Dotter et al. 2008) and removing stars
we identify as giants based on nonparametric and parametric Monte Carlo calculations we find a planet occurrence rate of ≃ 0.36 ± 0.08 for planets with radii
2R⊕ < RP < 32R⊕ and periods 1 < P < 50 days
per star in the temperature range 3400 < Tef f < 4100.
Using the KIC determined luminosity classes leads to a
somewhat lower planet occurrence of 0.26 ± 0.05.
4. The g − r colors of exoplanet host stars at J − H ≃
0.62 are consistent with an unbiased sample of Kepler
dwarf stars, ruling out any large difference between hosts
of Earth-to-Neptune sized planets and those without any
detected planets.
Surprisingly, there are hundreds of stars in our photometric sample that could have been easily identified as
giants with KIC photometry, but were assigned log g > 4.
The KIC primarily uses g −D51 vs g −r colors to identify
giants, and many late-type stars with KIC log g > 4.0
have g − D51 vs g − r colors consistent with giants (and
inconsistent with dwarfs).
Our calculated giant fraction is consistent with other
independent measurements. Gaidos et al. (2012) compare radial velocity data from M2K (Apps et al. 2010;
Fischer et al. 2012) to Kepler results and note that the
completeness of the coolest Kepler target stars may be
quite low (≃ 50%), much of which could be explained by
an underestimate of the frequency of giant stars. Additionally, Ciardi et al. (2011) find that bright Kepler M
stars are“predominantly giants, regardless of the KIC
classification” based on JHK photometry alone. Our
giant fraction is also consistent with the current understanding of Galactic structure: based on a simulation
from TRILEGAL (Girardi et al. 2005), ≃ 92 of stars
near the center of the Kepler field with KP < 14 and
KP − J > 2.0 are giants.
Interestingly, we find two KOIs with colors consistent
with giant stars. KOI 667 and KOI 977 both fall within
our giant training set in multiple color relations, and outside our dwarf training set. M11 identify KOI 977 as a
giant, and they also note that KOI 667 consisted of 5
objects within 6′′ which may be contaminating 2MASS
or WISE photometry. One of these objects could be an
eclipsing binary, diluted by the other stars. KOI 667
also has a relatively high (10%) false positive probability
based on Galactic structure models (Morton & Johnson
2011).
Our values of Tef f are consistent with results reported elsewhere also using BT-SETTL, including observations of the late-type KOIs with near-infrared spec-
Parameters of the Coolest Kepler Targets
13
Fig. 10.— Scatter plot of a sample of Kepler dwarf stars (blue triangles), giant stars (red circles), and giant stars labeled as dwarfs
(KIC log g > 4.0) by the KIC (black crosses) in g − r vs J − H space. An equal number of data points are shown from each subset
(giants/dwarfs/misidentified giants) to highlight the relative distributions. The histograms on the bottom and right side show the 1-D
distribution in each color (coloring matches the center plot). Histograms are normalized to a peak value of 1 and the median of each
histogram is marked with a dotted line (of the corresponding color). Although giant stars cover a range of J − H colors, those that
were mislabeled as dwarfs are more concentrated around J − H ≃ 0.61. The distribution of misidentified giants is bluer that the dwarf
distribution. Thus if the misidentified giant stars are not properly removed the dwarf sample will appear bluer (more metal poor) than the
KOI distribution (which contains almost no misidentified giants).
tra M11. These authors find a similar systematic offset
of 123+24
−32 K between their temperatures and KIC assigned temperatures. KIC temperatures are based on
the models of Castelli & Kurucz (2004) and the evolutionary tracks of Girardi et al. (2000), which, although
reliable for solar-mass stars, are untrustworthy for stars
with Tef f < 3750 K (Brown et al. 2011).
Our planet occurrence estimate is slightly higher than
that of H11, who, using results from Kepler, find a planet
occurrence rate of 0.30 ± 0.08 for stars with 3600 <
Tef f < 4100. The difference is primarily due to reliance on luminosity class determinations by Brown et al.
(2011), which we find to be inaccurate. However, the difference is within 1σ. For both our work and that of H11,
errors are dominated by the low number of late-type stars
(and therefore planets around them) in the Kepler field
and very high random (∼ 35%) errors in stellar radii.
In addition to random errors (e.g. stellar radii and
Rp /R∗ ) that are included in our Monte Carlo simulation,
there may be large systematic uncertainties in atmosphere models and evolutionary tracks, which can change
the resulting frequency. When we use the Yonsei-Yale
isochrones, it decreases our planet occurrence by ≃ 0.08.
Interestingly, this difference is similar in size to the random errors in our Monte Carlo analysis (≃ 0.08), and
the difference between proper giant removal and using
KIC log g > 4.0 (≃ 0.10). This suggests that giant star
removal, improved stellar characterization of the dwarf
stars, and use of reliable stellar models of late-type stars
are of roughly equal importance in characterizing the
planet occurrence around very cool stars.
The lack of a strong correlation between host-star
metallicity and the presence of Earth-to-Neptune sized
planets is consistent with what is found for solar-type
stars, e.g. Mayor et al. (2011). This also matches
the findings of M11, who determine that among the
late-type Kepler exoplanet hosts in our sample the median [M/H] is −0.11 ± 0.02. This distribution is consistent with stars in the solar neighborhood (−0.05 to
−0.15, Johnson & Apps 2009; Schlaufman & Laughlin
2010; Casagrande et al. 2011). A metallicity difference
could only be present if Kepler target stars are signifi-
14
Mann et al.
cantly more metal poor than stars in the solar neighborhood. As explained in Gaidos et al. (2012), Kepler late
K and M stars are < 250 pc from the Sun, and . 60 pc
above the galactic plane. Most of the stars will be in the
thin disk, and have metallicities similar to that of the
solar neighborhood.
Our analysis of the g − r colors of planet hosts contradicts the results of SL11, who find a 4σ difference
between g − r colors of late-type exoplanet hosts and
stars with no exoplanets present. Their result is most
likely an artifact of the large number of stars which were
misclassified as dwarfs in the KIC. SL11 state that their
result can be reproduced if their sample of KIC log g > 4
stars is between 10% and 30% giants, which they calculate by adding stars with KIC log g < 4 stars (test giant
stars) into their control sample, and measuring the resulting g − r color offset. We find that the giant fraction
is above 10% for this color range. Further, if the KIC
log g > 4 sample that SL11 used was significantly contaminated with giants, the sample will have bluer colors
than a true dwarf sample. Adding test giants (to measure the resulting color change) to an already giant-star
contaminated sample will create smaller changes in the
overall color of a sample than if the sample had contained only dwarf stars. Thus more test giant stars will
be required to produce a given color offset, creating an
artificially high estimate for the level of giant contamination required to produce the observed color difference.
Although the g − r colors of exoplanet hosts in our
sample are consistent with our dwarf sample, we cannot rule out small offsets (. 0.05) in g − r color. It is
possible that any metallicity effect is sufficiently small
that it is diluted to non-detection by the large number
of undetected exoplanets in the dwarf sample. As Kepler continues to discover planets of smaller radii and
at larger orbital periods, the answer may become more
clear.
This work was supported by NSF grant AST-0908419,
NASA grants NNX10AI90G and NNX11AC33G (Origins
of Solar Systems) to EG, as well as NSF grants AST 0607757 and AST 09-08419 to SL. We thank the anonymous
reviewer, whose thoughtful, quick, and thorough comments helped make this manuscript significantly better.
SNIFS on the UH 2.2-m telescope is part of the
Nearby Supernova Factory project, a scientific collaboration among the Centre de Recherche Astronomique
de Lyon, Institut de Physique Nuclaire de Lyon, Laboratoire de Physique Nuclaire et des Hautes Energies,
Lawrence Berkeley National Laboratory, Yale University, University of Bonn, Max Planck Institute for Astrophysics, Tsinghua Center for Astrophysics, and the
Centre de Physique des Particules de Marseille.
Some of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST). STScI is operated by
the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support
for MAST for non-HST data is provided by the NASA
Office of Space Science via grant NNX09AF08G and by
other grants and contracts.
Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation,
the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site
is http://www.sdss.org/.
This publication makes use of data products from the
Wide-field Infrared Survey Explorer, which is a joint
project of the University of California, Los Angeles,
and the Jet Propulsion Laboratory/California Institute
of Technology, funded by the National Aeronautics and
Space Administration.
Facilities: Kepler, MKO, UH2.2m, KPNO, MDM
REFERENCES
Aldering, G., et al. 2006, ApJ, 650, 510
Allard, F., Homeier, D., & Freytag, B. 2010, ArXiv e-prints
Allen, L. E., & Strom, K. M. 1995, AJ, 109, 1379
Apps, K., et al. 2010, PASP, 122, 156
Batalha, N. M., et al. 2010, ApJ, 713, L109
—. 2012, ArXiv e-prints
Bean, J. L., Seifahrt, A., Hartman, H., Nilsson, H., Wiedemann,
G., Reiners, A., Dreizler, S., & Henry, T. J. 2010, ApJ, 713, 410
Bessell, M. S., & Brett, J. M. 1988, PASP, 100, 1134
Borucki, W. J., et al. 2010, Science, 327, 977
—. 2011, ApJ, 736, 19
Bouchy, F., et al. 2009, A&A, 496, 527
Brown, T. M., Latham, D. W., Everett, M. E., & Esquerdo, G. A.
2011, AJ, 142, 112
Casagrande, L., Schönrich, R., Asplund, M., Cassisi, S., Ramı́rez,
I., Meléndez, J., Bensby, T., & Feltzing, S. 2011, A&A, 530,
A138
Castelli, F., & Kurucz, R. L. 2004, ArXiv Astrophysics e-prints
Cenarro, A. J., Cardiel, N., Gorgas, J., Peletier, R. F., Vazdekis,
A., & Prada, F. 2001a, MNRAS, 326, 959
Cenarro, A. J., Gorgas, J., Cardiel, N., Pedraz, S., Peletier, R. F.,
& Vazdekis, A. 2001b, MNRAS, 326, 981
Chabrier, G. 2003, PASP, 115, 763
Charbonneau, D., et al. 2009, Nature, 462, 891
Ciardi, D. R., et al. 2011, AJ, 141, 108
Cumming, A., Butler, R. P., Marcy, G. W., Vogt, S. S., Wright,
J. T., & Fischer, D. A. 2008, PASP, 120, 531
Danks, A. C., & Dennefeld, M. 1994, PASP, 106, 382
Demarque, P., Woo, J.-H., Kim, Y.-C., & Yi, S. K. 2004, ApJS,
155, 667
Dotter, A., Chaboyer, B., Jevremović, D., Kostov, V., Baron, E.,
& Ferguson, J. W. 2008, ApJS, 178, 89
Fabrycky, D. C., et al. 2012, ArXiv e-prints
Feiden, G. A., Chaboyer, B., & Dotter, A. 2011, ApJ, 740, L25
Fischer, D. A., & Valenti, J. 2005, ApJ, 622, 1102
Fischer, D. A., et al. 2012, ApJ, 745, 21
Fluks, M. A., Plez, B., The, P. S., de Winter, D., Westerlund,
B. E., & Steenman, H. C. 1994, A&AS, 105, 311
Gaidos, E., Fischer, D. A., Mann, A. W., & Lépine, S. 2012, ApJ,
746, 36
Gaidos, E., Haghighipour, N., Agol, E., Latham, D., Raymond,
S., & Rayner, J. 2007, Science, 318, 210
Gilbert, K. M., et al. 2006, ApJ, 652, 1188
Girardi, L., Bressan, A., Bertelli, G., & Chiosi, C. 2000, A&AS,
141, 371
Girardi, L., Groenewegen, M. A. T., Hatziminaoglou, E., & da
Costa, L. 2005, A&A, 436, 895
Gonzalez, G. 1997, MNRAS, 285, 403
Henry, T. J., Kirkpatrick, J. D., & Simons, D. A. 1994, AJ, 108,
1437
Howard, A. W., et al. 2010, Science, 330, 653
—. 2011, ArXiv e-prints
Jao, W.-C., Henry, T. J., Beaulieu, T. D., & Subasavage, J. P.
2008, AJ, 136, 840
Johnson, J. A., Aller, K. M., Howard, A. W., & Crepp, J. R.
2010, PASP, 122, 905
Parameters of the Coolest Kepler Targets
Johnson, J. A., & Apps, K. 2009, ApJ, 699, 933
Johnson, J. A., et al. 2012, AJ, 143, 111
Kennedy, G. M., & Kenyon, S. J. 2008, ApJ, 673, 502
Kraus, A. L., & Hillenbrand, L. A. 2009, ApJ, 703, 1511
Kraus, A. L., Tucker, R. A., Thompson, M. I., Craine, E. R., &
Hillenbrand, L. A. 2011, ApJ, 728, 48
Lançon, A., & Wood, P. R. 2000, A&AS, 146, 217
Lantz, B., et al. 2004, in Society of Photo-Optical
Instrumentation Engineers (SPIE) Conference Series, Vol. 5249,
Society of Photo-Optical Instrumentation Engineers (SPIE)
Conference Series, ed. L. Mazuray, P. J. Rogers, &
R. Wartmann, 146–155
Lépine, S., & Gaidos, E. 2011, AJ, 142, 138
Lépine, S., Rich, R. M., & Shara, M. M. 2007, ApJ, 669, 1235
Lépine, S., & Shara, M. M. 2005, AJ, 129, 1483
López-Santiago, J., Montes, D., Gálvez-Ortiz, M. C.,
Crespo-Chacón, I., Martı́nez-Arnáiz, R. M.,
Fernández-Figueroa, M. J., de Castro, E., & Cornide, M. 2010,
A&A, 514, A97
Mann, A. W., Gaidos, E., & Aldering, G. 2011, PASP, 123, 1273
Mayor, M., et al. 2011, ArXiv e-prints
Montes, D., Ramsey, L. W., & Welty, A. D. 1999, ApJS, 123, 283
Morton, T. D., & Johnson, J. A. 2011, ApJ, 738, 170
Muirhead, P. S., Hamren, K., Schlawin, E., Rojas-Ayala, B.,
Covey, K. R., & Lloyd, J. P. 2012, ApJ, 750, L37
Pereira, R., et al. 2010, in Proc. American Institute of Physics,
ed. J.-M. Alimi & A. Fuözfa, Vol. 1241, 259–266
15
Reid, I. N., & Hawley, S. L. 2005, New light on dark stars : red
dwarfs, low-mass stars, brown dwarfs, ed. Reid, I. N. & Hawley,
S. L.
Reid, I. N., Hawley, S. L., & Gizis, J. E. 1995, AJ, 110, 1838
Reid, I. N., et al. 2004, AJ, 128, 463
Rojas-Ayala, B., Covey, K. R., Muirhead, P. S., & Lloyd, J. P.
2012, ApJ, 748, 93
Santos, N. C., Israelian, G., & Mayor, M. 2004, A&A, 415, 1153
Schiavon, R. P., Barbuy, B., Rossi, S. C. F., & Milone, A. 1997,
ApJ, 479, 902
Schlaufman, K. C., & Laughlin, G. 2010, A&A, 519, A105
—. 2011, ApJ, 738, 177
Serote Roos, M., Boisson, C., & Joly, M. 1996, A&AS, 117, 93
Skrutskie, M. F., et al. 2006, AJ, 131, 1163
Sousa, S. G., et al. 2008, A&A, 487, 373
Torres-Dodgen, A. V., & Weaver, W. B. 1993, PASP, 105, 693
van Leeuwen, F. 2007, A&A, 474, 653
van Leeuwen, F., & Fantino, E. 2005, A&A, 439, 791
Vogt, S. S., Butler, R. P., Rivera, E. J., Haghighipour, N., Henry,
G. W., & Williamson, M. H. 2010, ApJ, 723, 954
West, A. A., et al. 2011, AJ, 141, 97
Wolfgang, A., & Laughlin, G. 2011, ArXiv e-prints
Woolf, V. M., & Wallerstein, G. 2006, PASP, 118, 218
Wright, E. L., et al. 2010, AJ, 140, 1868
Yanny, B., et al. 2009, AJ, 137, 4377